Bernard Jenkin, chairman of the public administration select committee, says a meeting will be held on Monday to decide if a hearing is required to assess her suitability.

The Tory MP for Harwich and North Essex said: "The committee has decided nothing formally until we meet.

"(But) I have spoken to a majority of the committee and those I have spoken to are in favour of holding such a hearing."

Ms Mills is currently head of the Department of Parliamentary Services (DPS) in Canberra.

The row took a sinister twist when it was revealed that officials in Ms Mills' department used CCTV cameras to spy on the office of an Australian senator as part of an investigation into a parliamentary official.

Image:Jack Straw is backing calls for a pre-appointment hearing

The Speaker is believed to want to bring in an outsider to press ahead with modernisation of the House, rather than promoting deputy clerk David Natzler.

It is thought 50 MPs, including former Foreign Secretary Jack Straw, are backing a motion tabled by Tory backbencher Jesse Norman calling for a pre-appointment hearing.

Downing Street upped the pressure on Mr Bercow by insisting the new clerk needs to have the backing of MPs.

A spokesman for the Prime Minister also confirmed he had yet to pass on the nomination to the Queen for approval.

The clerk earns £200,000 a year and combines the roles of constitutional adviser and Commons chief executive.

In an effort to defuse the row, Mr Bercow has indicated he wants to split the functions into two jobs as soon as possible.

However, his former deputy, Nigel Evans, says there will be "a lot of unhappy people" when the Commons returns unless there is a delay in the process.